There's nothing illegal about mocking the SEC on Twitter, but the inflammatory message was "very unwise" in the words of CFRA analyst Garrett Nelson in light of Musk's and Tesla's entanglements with the agency. The recent settlement, which requires that Musk pay a $20 million fine and step down as chairman of Tesla for three years, was considered by many to be a relatively light penalty, and separately, the agency is also looking into whether Tesla misled investors in reporting the extent of its Model 3 production issues.

Just want to that the Shortseller Enrichment Commission is doing incredible work. And the name change is so on point!

Under SEC rules, using social media for company disclosures is permitted as long as investors are alerted which accounts may make disclosures. In Tesla's case, the company had notified investors that Musk's official Twitter account may be used for additional disclosures about the company. As part of Musk's settlement with the SEC -- which is set to resolve accusations that Musk committed fraud in his 'funding secured' tweet from August -- Tesla is required to more closely monitor Musk's Twitter account to ensure false or improper disclosures.

But it isn't just business disclosures from Musk's account that have the power to move Tesla stock: Since his tweet late Thursday seeming to mock the SEC, Tesla's stock is down more than 7% as investors wonder about his stability and the board's ability to rein him in.

"The SEC may allow a company to use social media for company announcements, but it is a horrible idea unless there is strong board oversight," said David Reischer, a lawyer and CEO of legal services platform Legaladvice.com. "A single individual should not be tweeting on significant company events without a thorough review by the corporate board and a thorough legal review." And indeed, the SEC settlement calls for Tesla to institute a system for reviewing Musk's communications with investors before he sends them out.

Musk has often used his Twitter account to complain of short-sellers, and that again came to the fore in the Thursday tweet in which he called the SEC the 'Shortseller Enrichment Commission.' But the damage can extend well beyond that particular class of investors. Ross Gerber, CEO of the wealth management firm Gerber Kawasaki, said that he's received many alarmed emails from the firm's approximately 680 clients invested in Tesla, related to Musk's tweets.

"We're not an institution; our clients are regular people," he said. "It's a problem when I get emails from some of my biggest Tesla supporter clients who believe in the vision, questioning if [Musk] should be CEO anymore."

Gerber suggested the blurred lines between an executive's public personality and disclosures of formal information has the potential to cause chaos.

"I think for most CEOs there's not much to gain from Twitter; companies should have an official Twitter feed to publish information," he added. "It's an incredibly dangerous tool and people can't minimize how much damage it can cause."

While Musk may be an unusual case -- his Twitter account has more than 22 million followers, and he's among the most high-profile CEOs in the world -- few are making the case that CEOs going rogue on Twitter is especially wise.

"Musk put the SEC in a tight spot precisely because of his fame and influence," added Robin Allen, managing partner at Esperance Private Equity. "Regardless of the current socio-political climate, tweeting about securities is generally not recommended at all unless one is a registered broker or investment advisor."

Breaking up is hard to do, especially right now for Stamps.com, with its stock price nearly halved following a split with the U.S. Postal Service over the online shipper's demands for more independence.